Title (Use Title style here)
Retrospective GIS-Based Multi-Criteria Decision Analysis: A Case
Study of California Waste Transfer Station Siting Decisions
John F. Cirucci1, [email protected] A. Miller2,
[email protected] I. Blanford3, [email protected]
Pennsylvania State University, Department of Geography
(corresponding author)2The Pennsylvania State University,
Department of Geography, and Earth and Environmental Systems
Institute, University Park, PA3The Pennsylvania State University,
Dutton Institute of e-Education and GeoVISTA Center, Department of
Geography, University Park, PA
Abstract. Geographic information science (GIS) and multicriteria
decision analysis (MCDA) disciplines combine to provide valuable
insights which guide decision-makers evaluating complex spatial
criteria and alternatives, especially when there are conflicting
stakeholder values and objectives. Although GIS and MCDA methods
have been integrated to support forward-looking decision analyses,
there is also advantage to applying these methods retrospectively
in order to decipher the factors that composed previous
spatially-complex decisions. The objective of this study is to
demonstrate a methodology which applies retrospective GIS-based
MCDA to characterize decision-maker value preferences in past
siting decisions without a priori knowledge of the decision-making
process. As a representative case study, retrospective GIS-based
MCDA is performed on municipal solid waste transfer station site
decisions in Los Angeles County, California.
Potential attribute data were identified and compiled into a
geographic information system. The attributes of actual facility
sites and their surrounding vicinities were established as the
presence case for a positive decision. This decision problem was
structured considering two MCDA decision model types value function
using weighted linear combination and reference point. The
attributes of historical site selections were decomposed and
compared to unselected sites to identify attribute patterns. The
value function MCDA model was parameterized using logistic
regression to establish relative attribute weights which were
applied to create a probability spatial distribution profile. The
reference point MCDA rule model was parameterized contrasting
attribute relative frequency Pareto between transfer station and
general locations to create a satisfaction spatial distribution
profile. These resulting models provide both relative rank and
objective level of attributes represented in previous waste
transfer station location decisions. The methodology is applicable
to evaluation of spatial decisions in other domains, and can be
extended to consider other MCDA decision models.
Proceedings of the International Symposium on Sustainable
Systems and Technologies (ISSN 2329-9169) is published annually by
the Sustainable Conoscente Network. Jun-Ki Choi and Annick Anctil,
co-editors 2015. [email protected] 2015 by John
Cirucci, Justine Blanford, Douglas Miller Licensed under CC-BY
3.0.Cite as: Retrospective GIS-Based Multi-Criteria Decision
Analysis: A Case Study of California Waste Transfer Station Siting
Decisions. Proc. ISSST, Cirucci, J.F., Blanford, J.I., Miller, D.A.
(2015)
Introduction. Every day, we are constantly making simple
decisions, considering many criteria. Usually the process is
implicit and the decision maker is an individual. In contrast,
multicriteria decision analysis (MCDA) describes a collection of
formal approaches that can be used to make complex, high impact
decisions with multiple stakeholders. The general stages of an MCDA
process and two representative decision rule models are depicted in
Figure 1. As part of problem structuring, criteria and alternatives
are identified. Criteria can be system attributes or objectives
which fulfill a desired outcome. Alternatives are the options from
which a final decision is selected. There may be a few
alternatives, or an effective, infinite number such as with
continuous surface site selection. Problem structuring also
requires identification of stakeholders. A significant advantage of
many MCDA methods is explicit quantification of stakeholder values.
During the model building stage, decision rules are applied to
evaluate criteria so the relative worth of possible alternatives
can be characterized. Value measurement models entail assigning
partial values to all criteria then aggregating these through
various combination options to derive a comparative value for each
alternative. Reference point models involve establishing a
threshold, reference level for each criterion by which alternatives
are successively filtered. There are many variants on these and
other decision rule types. These two decision rule types were
examined in this study. The information that the decision rule
model yields is synthesized to establish a course of action (Belton
& Stewart, 2002). Figure 1. a) General MCDA Processb) Two
Decision Rule Model Types
Many decisions require spatial consideration criterion or
alternative characteristics may comprise location and proximity. A
geographic information system (GIS) can be used in multicriteria
decision analysis to assist decision-makers with spatial decisions,
and, in fact, GIS-based MCDA is an expanding field with increasing
research and application interest (Malczewski & Rinner, 2015).
Methodologies for GIS-based MCDA and MCDA, in general, deal
entirely with a forward-looking view, resolving a current problem
to achieve an improved future outcome. Alternatively, there could
be significant information derived from past decisions that
involved conflicting stakeholder objectives and complex evaluation
of alternatives.
Hypothesis. Thus, could evidence on historical, third-party
decisions be reverse-engineered to elicit information about the
stakeholders values and the decision-making process?
In this study, geospatial statistical analyses were integrated
with multiple criteria decision analysis methods to retrospectively
examine prior location decisions which entailed multiple
stakeholders with conflicting motivations and data uncertainty. An
inverse problem approach was applied to evaluate possible criteria,
develop value preference parameters and test different MCDA
decision rule models without explicit information about
stakeholders values or decision processes. The objectives were to
(1) create a probabilistic model for prediction of future related
decision outcomes; (2) provide insights in decision-maker
strategies; and (3) develop and demonstrate a new methodology
applicable to other spatial decision domains. The site selection of
municipal solid waste transfer stations (WTS) in Los Angeles
County, California, was selected as a representative case study.
Investigative Method. A WTS is a facility for solid waste to be
temporarily unloaded from collection vehicles and stored for a
short duration, so that it can be reloaded onto large load vehicles
for transportation to a final disposal facility (Environmental
Protection Agency, 2002). Siting a WTS is a classic NIMBY (not in
my backyard) scenario since residents and business owners will not
want to be proximate to the site. The decision maker for siting may
be a municipality or commercial entity but there are many
stakeholders influencing this decision. Transport distance and cost
are important siting considerations. However, there are many other
criteria which may be evaluated in decision analysis community
concern over noise, odor, and traffic, land use restrictions,
population density and growth rate, WTS capacity and technologies.
Some important social characteristics such as local population
ethnic and racial demographics may not be explicitly incorporated
into decision processes but may be implicitly correlated to
outcomes, so these must also be considered. Previous studies
identified WTS clustering in low income, non-white communities
(Environmental Protection Agency, 2000). There are inevitably other
site-specific criteria such as local political objectives and site
history which are difficult to broadly incorporate into a general,
county-wide study. For this study the data collection strategy was
to collect readily available, public information across a breadth
of categories. The effectiveness in these data describing actual
results will indicate the extent of deficiencies from missing
information and establish a baseline against which future criteria
can be evaluated. The study data consists of WTS location
coordinates, waste type, capacity, facility land area, landfill
disposal site coordinates, the complete county roadway network,
land use classification, elevation, population, demographics
(racial, ethnic, gender, age), housing characteristics, and income
level. The complete list of study criteria is included in the
Supplementary Material, Table S1.
Data Preparation. This study focused on WTS operating between
2000 - 2015 applying 2005 land use classification and 2010 Census
demographic data. The Solid Waste Information System (SWIS),
maintained by the California Department of Resources Recycling and
Recovery, served as the primary source of data on WTS and disposal
facilities in California (California Department of Resources
Recycling and Recovery, 2014). Effective after 1994, the only WTS
in California that require full permits are those with greater than
100 tons per day capacity, designated as Large Volume Transfer
Stations. For the purpose of this study, 41 large volume WTS
operating in Los Angeles County (contiguous, excluding islands)
between 2000 and 2015 were analyzed.
Demographic data and associated TIGER/Line shapefile geographic
boundaries were obtained from the U.S. Census Bureau database at
the census block level for 2010 and included age, gender, race,
ethnicity and household characteristics (family size, ownership
type. Income and poverty level were acquired from the U.S. American
Community Survey 5-year estimates available at the block group
level for Los Angeles County (United States Census Bureau, 2015).
Roads were also obtained as MAF/TIGER line shapefiles from the US
Census Bureau. Slope data were calculated using the 10-foot Digital
Elevation Model (DEM) obtained from the Los Angeles Regional
Imagery Acquisition Consortium (Los Angeles County, 2015). Land use
data for 2009 were obtained from SCAG (Southern California
Association of Governments, 2015).
Since transportation costs are important in the optimization of
site selection (Environmental Protection Agency, 2002), this was
accounted for by calculating travel time from each cell to all
disposal locations within the LA County. The travel time to
residents was estimated based on the road distance to serve a
population of 60,000 people. Road types not suitable for transfer
vehicles, such as bike paths were removed; the remaining road types
were assigned a relative transportation cost represented as
estimated travel time (Table S2 Supplementary).
All data were spatially converted and assigned to 1 hectare area
cells. The contiguous LA County land area is over 1 million
hectares. These cells were established as the set of possible site
alternatives. The median land area of a transfer station is 2.5
acres in LA County which is approximately consistent with this
study area cell resolution. Demographic data (e.g. population,
housing, income) and land use at an immediate cell location may not
be indicative of the vicinity characteristics. Therefore, the data
for the surrounding neighborhood (within a radius of 0.25 km) was
obtained and the mean value was assigned to each center cell. All
data were extracted to tabular format for subsequent statistical
analyses.
Analysis. Data analyses were performed using ArcGIS 10.2, R
version 3.0.2 (R Core Team, 2013) and Excel. A preliminary
evaluation of the spatial distribution of WTS in LA County was
performed in ArcGIS to identify the extent of non-random
distribution and clustering. All attribute data were mapped for
visual examination and qualitative pattern identification. Tabular
attribute data was examined as boxplots, histograms and density
plots. Side-by-side comparison was made for WTS locations versus
general locations considering general statistical characteristics
range, mean, median, skew, standard deviation. Mean difference and
Chi-squared test probabilities were computed. Two general MCDA
decision rule models were evaluated using this dataset: Value
Function type and Reference Point type.
Value Function Decision Model. For the value function model
form, a simple weighted linear combination was considered. Data
were regressed to establish attribute weights which provide a sum
of products value for any given location alternative. Higher values
should correspond to more preferred locations. The dependent
variable is the presence indication of a transfer station at a
given location, represented as 1 or 0, for present or not present,
respectively. Since this outcome is binary, a logistic regression
was performed. Attributes were fitted to the model form:
ytransfer = 1 / [1+ exp-(c0 +c1x1 + c2 x2 +)]
Where, ytransfer = probability of the WTS presence, xi =
attribute i value, ci = attribute i weight.
Logistic regression model goodness-of-fit was evaluated
considering changes in residual deviance versus null deviance.
Relative comparisons of model forms were performed using deviances
(log likelihood ratios) and Akaike information criteria (AIC).
Attribute significance and collinearity were evaluated considering
P-value, variance inflation factor (VIF) and condition indices
(Hosmer, Lemeshow, & Sturdivant, 2013). AIC represents a
trade-off between model fit and collinearity, and was used as the
final optimization parameter. Individual attributes were
iteratively removed based on lowest rank confidence of statistical
mean difference between WTS and general locations, evidence of
collinearity, and stepwise improvement in fit. Attribute
combinations were evaluated and removed iteratively to
progressively improve model fit and reduce multicollinearity.
Linear combination of the sum product of weights and attribute
values provide the logit value which was then transformed into a
WTS logistic probability assigned to each cell. This table of
probabilities retaining its spatial georeferences was imported back
into ArcGIS to produce a WTS probability distribution map for LA
County.
Reference Point Decision Model. The reference point decision
rule model required the identification of significant maximum or
minimum attribute thresholds. These were fitted by comparison of
the attribute ranges and distribution profiles of actual WTS
locations versus general locations. For each attribute, relative
frequency (frequency/total) Pareto plots of WTS locations and
general locations were created using the 41 WTS attribute values as
bin increments. From these, the WTS:general relative frequency
ratio was computed as a function of attribute value. Ratios greater
than one imply that an attribute has a negative impact that is, the
frequency is increasing faster for WTS locations than for general
locations over an attributes range. The opposite holds true for
relative frequency ratios less than one. These are consistent with
the mean difference analyses. Potential attribute reference points
are indicated when there is a discontinuity or change in slope
toward unity for these ratios. The reference point is a maximum
threshold for ratios > 1 and a minimum threshold for ratios <
1. Reference points are not necessarily indicated for all
attributes and some threshold indications were indistinct. For this
study, obvious reference points were classified as tier 1. Weak
reference points defined as those which occurred when WTS relative
frequency was less than 50% or when there was variability in the
slope change were classified as tier 2. These reference points were
applied to classify attributes for all cells in the full dataset.
In ArcGIS the individual attribute raster layers were reclassified
from a value range to a binary indication of a reference point
satisfaction (1= satisfied, 0=not satisfied). These individual
attribute, binary raster layers were then processed to three
different spatial distributions: Product of all tier 1 binary
reference point raster layers Product of all tier 1 and 2 binary
reference point raster layers Sum of all tier 1 and 2 binary
reference point raster layers
The two product combinations represent a conventional reference
point decision rule resulting in a binary outcome for WTS
satisfaction. The combined tier 1 and 2 rasters is most
restrictive. The sum combination is a non-conventional reference
point decision rule but provides a satisfaction gradient.
The value measurement probability results and reference point
satisfaction results were mapped across LA County to provide a
visualization of their distributions and comparative responses.
RESULTS. Spatial distribution analysis of the active large
volume WTS revealed a non-random distribution within LA County with
an average mean distance of 3.1 km between stations versus a random
distributed distance of 4.6 km. A low p-value (0.000084) and large
negative z-score (-3.933) indicated low probability of random
distribution and an observed mean distance between stations at
about 2 standard deviations below a random distribution level. This
was expected since WTS were seen to be clustered in proximity to
the higher population density areas. Statistical comparison of
attributes for WTS locations versus general locations indicate
>95% confidence of significant mean difference for 19 of the 27
attributes (Supplemental Information Table S3).
The retrospective value measurement logistic regression
initially fit all attributes (27) as a baseline giving expectedly
poor fit. Following 17 model improvement iterations, the final form
was resolved comprising 11 attributes with significant,
non-collinear model contribution. The value measurement probability
distribution and normalized attribute weights are shown in Figure
2. Transportation times which directly impact WTS operating
economics dominate the model fit. However, 6 demographic/social
attributes significantly and independently impact WTS probability.
This does not directly implicate causality in the decision process
but these attributes are not collinear with other study attributes.
The absolute value preference probabilities are quite low, less
than 0.02. This is expected since there is a small, discrete number
of WTS required across the county yielding a randomly distributed
probability of only 0.00004. Figure 2. Normalized Attribute Weights
and Value Measurement Probability Distribution
Retrospective reference point evaluation yielded 7 tier 1
attributes and 4 tier 2 attributes. 8 of these attributes were
consistent with the value measurement results. The resulting
satisfaction distributions for the three alternate reference point
treatments are shown in Figure 3. Tier 1 and tier 1&2 products
satisfied only 52% and 39% of actual WTS locations, respectively.
However, these satisfaction frequencies were much higher than
general locations, at 9% and 3%.
a) Tier 1 Product Layerb) Tier 1 & 2 Product Layerc) Tier 1
& 2 Sum LayerFigure 3. Reference Point Satisfaction
Distribution for Los Angeles County WTS Discussion. Retrospective
value measurement analysis provided a well-fit probabilistic model
predicting greater than 40 times mean higher probability for actual
WTS site locations, and confirming the significance of
transportation economic contribution while also indicating social
demographic bias in decision outcomes. Retrospective reference
point satisfaction was a simpler, non-regression method. Since the
product aggregation of reference points is a restrictive
filtration, the proportion of satisfactory sites becomes small as
the number of attributes increases, so this approach might be best
suited for decisions with a limited number of well-defined
attributes. Both methods yielded practical and reasonably
consistent results. In addition to further enhancement on these
retrospective methods, useful future research should explore other
MCDA methods such as outranking and the analytical hierarchy
process.
Acknowledgements. This study was not funded.
ReferencesBelton, V., & Stewart, T. (2002). Multiple
criteria decision analysis: an integrated approach.
Kluwer.California Department of Resources Recycling and Recovery.
(2014, November 12). Solid Waste Information System (SWIS).
Retrieved from CalRecyle:
http://www.calrecycle.ca.gov/SWFacilities/Directory/Default.htmDepartment
of Regional Planning, County of Los Angeles. (2015, March). Plans
& Ordinances. Retrieved from Department of Regional Planning:
http://planning.lacounty.gov/plans/adoptedEnvironmental Protection
Agency. (2000). A regulatory strategy for siting and operating
waste transfer stations. Environmental Protection Agency. (2002).
Waste transfer stations: a manual for decision-making. Los Angeles
County. (2015, March). 2006 10-foot Digital Elevation Model (DEM)
LAR-IAC Public Domain. Retrieved from Los Angeles County GIS Data
Portal:
http://egis3.lacounty.gov/dataportal/2011/01/26/2006-10-foot-digital-elevation-model-dem-public-domain/Malczewski,
J., & Rinner, C. (2015). Multicriteria Decision Analysis in
Geographic Information Science. New York: Springer.R Core Team.
(2013). R: A language and environment for statistical. Retrieved
from R Foundation for Statistical Computing, Vienna, Austria:
http://www.R-project.org/Southern California Association of
Governments. (2015, March). GIS Library. Retrieved from GIS and
Data Services:
http://gisdata.scag.ca.gov/Pages/GIS-Library.aspxUnited States
Census Bureau. (2015, April). American Community Survey. Retrieved
from US Census:
http://www.census.gov/acs/www/data_documentation/data_via_ftp/United
States Census Bureau. (2015, March). TIGER Products. Retrieved from
http://www.census.gov/geo/maps-data/data/tiger.html
Retrospective GIS-Based Multi-Criteria Decision Analysis: A Case
Study of California Waste Transfer Station Siting Decisions
Cirucci et al.
Supplementary Information
Retrospective GIS-Based Multi-Criteria Decision Analysis: A Case
Study of California Waste Transfer Station Siting Decisions
John F. Cirucci The Pennsylvania State University,
[email protected] A. Miller The Pennsylvania State
University, [email protected] I. Blanford The Pennsylvania
State University, [email protected]
AttributesThe attribute criteria for which decision rules were
evaluated are listed in Table S1.
Table S1. Final Attribute Data Evaluated in Decision Rule
ModelsField NameDescriptionTypeCategory
OBJECTIDfeature identificationordinalidentifier
Transfer2015transfer station present (1,0)ordinalclassifier
Disposal2010disposal facility present (1,0)ordinalclassifier
LandUse05SCAG land use aggregate code at
locationnominalclassifier
TimeDispNrTime Distance to nearest disposal
facilityratioattribute - distance
TimeDispMnMean Time Distance to all disposal
facilityratioattribute - distance
TimePop60k250Time (Cost Distance) to nearest 60000
populationratioattribute - distance
PopDens250Population near (population per km2)ratioattribute -
demographic
PopFrWh250Population fraction White at radius nearratioattribute
- demographic
PopFrBl250Population fraction Black at radius nearratioattribute
- demographic
PopFrAs250Population fraction Asian at radius nearratioattribute
- demographic
PopFrHi250Population fraction Hispanic/Latino origin
nearratioattribute - demographic
PopFrFem250Population over 20 years old fraction female
nearratioattribute - demographic
MednAge250Median age nearratioattribute - demographic
HousDens250Housing units near (housing units per
km2)ratioattribute - housing
HousFrVac250Housing units fraction vacant nearratioattribute -
housing
HousFrRnt250Housing units occupied fraction rented
nearratioattribute - housing
HousAvgSz250Average household size of occupied housing units
nearratioattribute - housing
SlopePercent sloperatioattribute - terrain
LU05COM250Fraction commercial land use nearratioattribute - land
use
LU05PUB250Fraction public land use nearratioattribute - land
use
LU05MIL250Fraction military land use nearratioattribute - land
use
LU05IND250Fraction industrial land use nearratioattribute - land
use
LU05TRN250Fraction transportation and utility land use
nearratioattribute - land use
LU05REC250Fraction recreational land use nearratioattribute -
land use
LU05AGR250Fraction agricultural land use nearratioattribute -
land use
LU05WAT250Fraction water land use nearratioattribute - land
use
LU05VAC250Fraction vacant land use nearratioattribute - land
use
LU05RES250Fraction residential land use nearratioattribute -
land use
PovertyFrac250Fraction individuals below poverty level
nearratioattribute - affluence
IncomePerCap250Income per capita nearratioattribute -
affluence
Travel Time EstimationRoad data acquired as MAF/TIGER shapefiles
included class codes. These were aggregated and assigned cost
factors as shown in Table S2. A nominal speed limit was applied to
these road types. An integer value cost factor was set, inversely
proportional to the nominal road speed. Travel time was
approximated from the cost factor as given in Equation S1.
(Equation S1)
Allocation to each waste transfer station was made on the basis
of population, not land area. Municipal solid waste generation per
capita has been relatively flat since 1990 but recycle and compost
recovery has been increasing so that net disposal has fallen from
1.7 to 1.3 kg per person from 1990 to 2012 (Environmental
Protection Agency, 2014). On the basis of 1.5 kg per person, a
California large volume transfer station operating at the minimum
permit capacity of 100 tons per day would serve about 60,000
residents. This was used as the reference population level for any
potential transfer station location to determine an impact radius
as Euclidean distance and travel time based on road network. For
consideration of the transportation time between population
locations and potential WTS locations, both population density and
transportation cost factor were taken together. A representative
criteria, t60kPop was established to serve as a surrogate value for
transportation time to serve 60,000 individuals as given in
Equation S2. This was first established for each cell then averaged
for the surrounding neighborhood within a radius of 0.25 km.
(Equation S2)
Table S2. Relative Roadway Cost Factors Based on MAF/TIGER
Feature Class Codes
MTFCCFeature ClassNominal Speed LimitCostFactor
S1100Primary Road603
S1200Secondary Road454
S1400Local Neighborhood Road, Rural Road, City Street1512
S1500S1630S1640S1730S1740Vehicular Trail (4WD)RampService Drive
usually along a limited access highwayAlleyPrivate Road for service
vehicles536
NullNo road--360
Preliminary Summary StatisticsSummary statistics for attribute
data including comparison of WTS and general locations is shown in
Table S3. The mean difference Z-score was calculated per equation
S3. This is a dimensionless difference between WTS and general
attribute values normalized based on their standard deviations. An
associated p-value represents the probability that there is no
significant mean difference (null hypothesis). Hence a p-value less
than 0.05 indicates a 95% confidence the difference of the means is
significant. However, most of these attribute data were not
normally distributed causing skew in the Z-score. Therefore, a
Chi-squared p-value was also determined. The Chi-square test was
applied to attribute frequency divided into bins corresponding to
the general data quartile breaks.
(Equation S3)Where
There were 21 attributes that presented 95% confidence for
significant mean difference between WTS and general locations.
Table S3. Attribute Comparison between Transfer Station
Locations and All LocationsAttributeTransfer Station Locations
(n=41)All Locations (n=1027377)Z-score
mean/SDP-valueZ-scoreP-value2 Test
MeanMedianStandardDeviationMeanMedianStandardDeviation
TimeDispNr989326464168732-89.40.00000.0000
TimeDispMn23722926608315727-89.70.00000.0000
TimePop60k25039060361110900673573306004523278749-221.00.00000.0000
PopDens250776286115295022161-1.00.24950.0035
PopFrWh2500.540.560.260.670.720.27-3.10.00280.0117
PopFrBl2500.090.020.150.060.010.150.90.27340.3422
PopFrAs2500.090.040.180.090.020.160.00.39890.4174
PopFrHi2500.550.640.370.280.170.284.30.00000.0000
PopFrFem2500.450.500.160.480.500.14-1.00.25380.1772
MednAge25035.631.88.943.143.511.9-4.90.00000.0003
HousDens250258794593331811-1.00.23200.0058
HousFrVac2500.050.030.100.150.050.23-5.70.00000.0210
HousFrRnt2500.610.530.300.320.210.315.50.00000.0000
HousAvgSz2503.393.331.412.782.751.092.40.02220.0094
Slope1.60.92.415.37.217.9-37.30.00000.0000
LU05COM2500.040.000.090.020.000.101.00.24490.0087
LU05PUB2500.010.000.030.020.000.08-1.70.10150.6080
LU05MIL2500.000.000.000.020.000.13-145.70.00000.8152
LU05IND2500.650.690.280.030.000.1414.10.00000.0000
LU05TRN2500.170.080.200.030.000.124.70.00000.0000
LU05REC2500.000.000.000.010.000.07-128.10.00000.7775
LU05AGR2500.010.000.050.030.000.16-2.40.01990.3920
LU05WAT2500.000.000.000.010.000.08-113.00.00000.8623
LU05VAC2500.020.000.050.610.920.45-73.20.00000.0000
LU05RES2500.080.000.180.190.000.33-4.10.00010.0056
PovertyFrac2500.220.220.120.120.090.114.90.00000.0000
IncomePerCap250227371923410950342753024619080-6.70.00000.0008
Null hypothesis probability > 5%
Attribute data were also examined visually through boxplots and
histograms. Four representative histograms generated in R are shown
in Figure S1.
a) Mean Travel Time to All Disposal Facilitiesb) Travel Time to
60000 Residents c) Population Fraction White (within 0.25 km)d)
Population Fraction Hispanic (within 0.25 km)Figure S1. Boxplot
Comparison between WTS Locations and General Locations in LA
County
Value Measurement Decision RuleThe logistic regression performed
to determine value measurement attribute coefficients proceeded
through 17 iterations with the goal to attain goodness of fit while
minimizing multicollinearity between attributes. The progression of
these iterations is summarized in Table S4.
The final iteration resulted in coefficients that were then
applied in the logistic form to derive a WTS probability for each
cell in the study area. A small scale map of this probability
distribution covering the City of Los Angeles is depicted in Figure
S2 showing good correspondence with all current WTS locations.
Table S4. Value Measurement Logistic Regression Iteration
Log
RUN01234567891011121314151617
Dresid912.6486.7490.9493.2516.4516.5490.6503.4490.7490.7490.7490.7490.8490.9490.8490.9518.3491.2
Dnull912.6684.4684.4684.5684.5684.5684.4684.4684.4684.4684.4684.4684.4684.4684.4684.4724.9684.4
R2L0.0000.2890.2830.2790.2460.2450.2830.2640.2830.2830.2830.2830.2830.2830.2830.2830.2850.282
AIC914.57542.70530.90527.20542.40540.50530.58539.37528.65526.66524.70522.73520.77520.87518.79516.89542.34515.18
Paic0.00000.00000.00040.00250.00000.00000.00050.00000.00120.00320.00860.02290.06110.05810.16450.42530.00001.0000
signif var002211222222222222
VIF>7.5055200301000000000
COEFFICIENTS
Intercept-10.13-11.01-8.87-9.81-8.28-8.40-10.75-6.62-10.70-10.56-10.64-10.82-10.86-10.96-10.82-10.91-9.68-11.27
TimeDispNr0.00E+001.29E-029.95E-030.00E+00-7.78E-030.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
TimeDispMn0.00E+00-1.86E-02-1.48E-02-5.96E-03-1.74E-06-7.90E-03-5.73E-03-7.91E-03-5.72E-03-5.75E-03-5.89E-03-5.95E-03-5.96E-03-5.95E-03-6.00E-03-5.98E-03-6.61E-03-5.64E-03
TimePop60k2500.00E+00-1.69E-06-1.47E-06-1.54E-060.00E+00-1.70E-06-1.45E-06-1.62E-06-1.47E-06-1.47E-06-1.49E-06-1.48E-06-1.47E-06-1.45E-06-1.47E-06-1.45E-06-1.32E-06-1.39E-06
PopDens2500.00E+00-1.54E-04-1.64E-040.00E+000.00E+000.00E+00-1.61E-04-1.53E-04-8.67E-05-8.17E-05-7.04E-05-6.96E-05-6.95E-05-7.20E-05-7.09E-05-7.40E-05-6.52E-050.00E+00
PopFrWh2500.000-0.0960.006-0.080-0.301-0.2630.0000.0000.0000.0000.0000.0000.0000.0350.0000.0000.0000.000
PopFrBl2500.000-0.4630.0000.0000.0000.000-0.353-0.309-0.367-0.370-0.364-0.363-0.3800.000-0.3770.0000.0000.000
PopFrAs2500.00000.04700.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000
PopFrHi2500.0000.4130.5480.5790.8960.8140.4120.5770.3830.3830.3900.3540.3610.4590.3590.4620.1340.450
PopFrFem2500.001.120.000.000.000.001.050.811.041.041.051.061.101.111.111.110.231.11
MednAge2500.0000-0.0194-0.0206-0.01800.00000.0000-0.0194-0.0186-0.0195-0.0194-0.0193-0.0172-0.0172-0.0171-0.0172-0.0168-0.0270-0.0161
HousDens2500.00E+002.49E-042.26E-04-7.30E-05-7.54E-04-7.49E-042.19E-040.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
HousFrVac2500.000-0.586-0.841-0.475-0.379-0.275-0.533-0.616-0.471-0.478-0.520-0.4320.0000.0000.0000.0000.0000.000
HousFrRnt2500.0000.2430.1490.3430.9420.9520.2730.3650.2880.2810.2730.2940.3010.3070.3120.3180.0000.275
HousAvgSz2500.0000-0.0416-0.0377-0.0413-0.04190.0000-0.0258-0.0518-0.0345-0.0339-0.03340.00000.00000.00000.00000.00000.00000.0000
Slope0.0000-0.0575-0.0596-0.0631-0.0822-0.0822-0.0605-0.0521-0.0607-0.0606-0.0641-0.0638-0.0636-0.0624-0.0645-0.0631-0.0674-0.0599
LU05COM2500.0002.7500.3720.151-1.429-1.3880.267-3.2630.2970.1410.2460.2720.2670.2560.0000.0000.0000.000
LU05PUB2500.001.280.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00
LU05MIL2500-1500000000000000000
LU05IND2500.008.015.715.813.923.945.782.385.775.645.745.755.765.735.725.695.805.97
LU05TRN2500.007.655.295.390.000.005.440.005.435.295.405.425.425.405.385.365.645.65
LU05REC2500-1580000000000000000
LU05AGR2500.005.260.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00
LU05WAT2500-1600000000000000000
LU05VAC2500.0002.060-0.208-0.1440.0000.000-0.253-3.714-0.275-0.4160.0000.0000.0000.0000.0000.0000.0000.000
LU05RES2500.0002.4690.254-0.0430.0000.0000.236-3.1490.2070.0000.0000.0000.0000.0000.0000.0000.0000.000
PovertyFrac2500.002.062.010.000.000.002.342.022.312.312.282.282.252.182.242.172.212.03
IncomePerCap2500.00E+001.18E-051.18E-057.96E-061.33E-061.33E-061.15E-058.49E-061.18E-051.19E-051.22E-051.22E-051.21E-051.23E-051.20E-051.23E-051.03E-051.28E-05
Figure S2. Value Measurement WTS Probability Distribution, City
of Los Angeles
Reference Point Decision RuleThe relative frequency ratio
analysis described in the main paper is represented graphically for
two attributes in Figures S3 and S4. In Figure S3 the ratio for
vacant housing fraction indicates a distinct slope change at an
attribute level of 0.06. This was interpreted as a reference point
maximum threshold.
Figure S3. Relative Frequency Ratio WTS:General Location for
Vacant Housing Fraction
In Figure S4 the ratio for industrial land use fraction is
shown. Although there is a significant mean difference between WTS
and general locations, there is no distinct discontinuity in the
ratio, hence no reference point threshold was identified.
Figure S4. Relative Frequency Ratio WTS:General Location for
Industrial Land Use Fraction
The reference point values were applied to the study area and
each cell classified according to three different reference point
aggregation forms. The frequency of satisfactory designations for
WTS and general locations is shown Figure S5.
Figure S5. Reference Point Satisfaction Frequency WTS vs.
General Location Comparison
The reference point satisfaction distribution for the City of
Los Angeles is depicted in Figures S6, S7 and S8 for the tier 1
product, tier 1&2 product and tier 1&2 sum aggregation
methods, respectively.
Figure S6. Reference Point Tier 1 Product Satisfaction
Distribution, City of Los Angeles
Figure S7. Reference Point Tier 1 & 2 Product Satisfaction
Distribution, City of Los Angeles
Figure S8. Reference Point Tier 1 & 2 Sum Satisfaction
Distribution, City of Los Angeles